

\magnification = 2200 %\magstep3 

\def\UseTimesRoman{
\font\cmr=Times
\font\TR=Times at 10pt
\font\TRXII=Times at 12pt
\font\TRXIV=Times at 14pt
\font\TRXX=Times at 20pt
\font\TRXXIV=Times at 24pt
\font\TI=TimesI at 10pt     %Times Italic
\font\TB=TimesB at 10pt     %Times Bold
\font\TBI=TimesBI at 10pt   %Times Bold Italic
\font\TBIviii=TimesBI at 8pt
\font\TBIv=TimesBI at 5pt
%\font\TO=TimesO at 10pt  %Times Oblique (Times Roman, slanted 22% 
with EdMetrics)
\font\TO=TimesI at 10pt  %Times Oblique (Times Roman, slanted 22% 
with EdMetrics)

\font\TIVIII=TimesI at 8pt
\font\TRVIII=Times at 8pt
\font\TIVI=TimesI at 6pt
\font\TRVI=Times at 6pt

	     \font\tenrmscld=Times at 10 pt
       \font\sevenrmscld=Times at 7 pt
       \font\fivermscld=Times at 5 pt

       \font\teniscld=cmmi10 at 10.3 pt
       \font\seveniscld=cmmi10 at 7.21 pt
       \font\fiveiscld=cmmi10 at 5.15 pt
       \font\tensyscld=cmsy10 at 10.3 pt
       \font\sevensyscld=cmsy10 at 7.21 pt
       \font\fivesyscld=cmsy10 at 5.15 pt
       \font\tenexscld=cmex10 at 10.3 pt
       \font\tenbfscld=cmbx10 at 10.3 pt
       \font\sevenbfscld=cmbx10 at 7.21 pt
       \font\fivebfscld=cmbx10 at 5.15 pt

\font\Courier = Courier
\font\Symbol = Symbol

\def\Omega{\hbox{{\Symbol W}}}

\textfont0=\tenrmscld \scriptfont0=\sevenrmscld\scriptscriptfont0=\fivermscld
\def\rm{\fam0\tenrmscld}
\textfont1=\teniscld \scriptfont1=\seveniscld \scriptscriptfont1=\fiveiscld
\def\mit{\fam1} \def\oldstyle{\fam1\teni}
\textfont2=\tensyscld \scriptfont2=\sevensyscld \scriptscriptfont2=\fivesyscld
\def\cal{\fam2}
\textfont3=\tenexscld \scriptfont3=\tenexscld \scriptscriptfont3=\tenexscld
\def\it{\TI}
\def\sl{\TO}
\def\bf{\TB}
\def\rm{\TR}
%\def\tt{\ttCourier}
\def\tt{\Courier}
\def\abstractfont{\TRVIII}
\def\footnotefont{\TRVIII}
\def\tinyfont{\TRvi}
\def\smalltitlefont{\TRXII}
\def\titlefont{\TRXIV}
\def\bigtitlefont{\TRXX}
\def\verybigtitlefont{\TRXXIV}
\textfont9=\TBI \scriptfont9=\TBIviii \scriptscriptfont9=\TBIv
\def\mbi{\fam9}
\rm
}

%\UseTimesRoman

\hsize 7 true in
\vsize 9 true in
\hoffset = -0.20 true in
\voffset -0.25 true in
\parskip=3pt

\overfullrule = 0pt



\input amssym.def            % small letters for UNIX,  not: AMSsym.def
\input epsf.def% \input epsf %for UNIX
%\input epsf          %\input epsf.def for MAC f"ur BILDER!!

\input BoxedEPS
\SetTexturesEPSFSpecial
\HideDisplacementBoxes

\def\lf{\ \hfil\break}       % Neue Zeile ohne Einr"ucken, 'linefeed'
\def\cl{\centerline}
\def\LF{\medskip\noindent}   % Neue Zeile mit breiterem Zwischenraum


\nopagenumbers

\vglue 10pt



\cl {\bf Genus 2 Knots}
\LF
\cl{See also Torus Knots.}
\LF
Torus knots are the most easily described knots and, in particular when
viewed on a torus, they are also very easy to visualize. \lf
If one wants to visualize other knots on some surface, one needs more
complicated surfaces than tori. From this point of view the next simplest
knots can be put on a genus 2 surface. The surface we chose looks like
two tori which are joined by a small handle. (The size of these tori is
controlled by the parameters aa and bb as for torus knots.) The surface
is implicitly described by an equation (see implicit surfaces in the surface
category) and can be made fatter by increasing ff. As examples of
genus 2 knots we chose the connected sums of two (dd, ee) - torus knots.
The sign of hh controls whether the two torus knots are connected with
reflectional symmetry or with $180^\circ$ rotational symmetry. The two
simplest examples are the {\it Square Knot} and the {\it Granny Knot}
where two (3, 2) - torus knots (Trefoil Knots) are connected with the two 
types of symmetry.

\vfill\eject

\bye
